invalid ballots and electoral competition

ECARES ULB - CP 114/04

50, F.D. Roosevelt Ave., B-1050 Brussels BELGIUM www.ecares.org

Endogenous Enforcement Institutions

Gani Aldashev SBS-EM, ECARES, Université libre de Bruxelles and CRED, University of Namur

Giovanni Mastrobuoni University of Essex and Collegio Carlo Alberto

October 2015

ECARES working paper 2015-39

Invalid Ballots and Electoral Competition∗

Gani Aldashev†and Giovanni Mastrobuoni‡

October 24, 2015

Abstract

In close elections, a sufficiently high share of invalid ballots - if driven by votermistakes or electoral fraud - can jeopardize the electoral outcome. We study how thecloseness of electoral race relates to the share of invalid ballots, under the traditionalpaper-ballot hand-counted voting technology. Using a large dataset from the Italianparliamentary elections in 1994-2001, we find a strong robust negative relationshipbetween the margin of victory of the leading candidate over the nearest rival andthe share of invalid ballots. We argue that this relationship is not driven by votermistakes, protest, or electoral fraud. The explanation that garners most supportis that of rational allocation of effort by election officers and party representatives,with higher rates of detection of invalid ballots in close elections.

Keywords: vote counting; invalid ballots; election officers; party representativesJEL classification codes: D72; D73;

∗We thank Enriqueta Aragones, Georg Kirchsteiger, Jim Snyder, and seminar participants at CollegioCarlo Alberto and the University of Padua for useful comments.

†Corresponding author. Universit libre de Bruxelles (ULB), ECARES, and CRED, Universityof Namur. Mailing address: 50 Avenue F Roosevelt, CP 114, 1050 Brussels, Belgium. Email:[email protected] .

‡Department of Economics, University of Essex and Collegio Carlo Alberto. Mailing address: Wiven-hoe Park, CO43SQ Colchester, UK. Email: [email protected].

“It’s not the voting that’s democracy, it’s the counting” (Stoppard, 1972)

The heated debate in policy-making and academic circles following vote-counting prob-

lems at the 2000 U.S. Presidential elections (Caltech and MIT Voting Technology Project,

2001, Knack and Kropf, 2003, Ansolabehere and Stewart III, 2005, Wand et al., 2001,

Card and Moretti, 2007) indicates that the organization of ballot casting and counting is

at the heart of democratic elections. During the last decade, numerous countries carried

out important policy changes regarding how voting and vote counting is organized. Under

the Help America Vote Act (HAVA), for instance, the U.S. invested around 3 billion USD

into improving and replacing voting technologies (Stewart III, 2011).

In general, in most large elections, there is a relatively small fraction of votes that

is counted as invalid. When electoral race is tight, even a small number of votes can

make a difference for the electoral outcome, and thus the importance of invalid ballots

increases disproportionately. Intuitively, if the share of invalid ballots is sufficiently high

as compared to the margin of victory of the winning candidate, and is driven by voter

mistakes or electoral fraud, then invalid ballots might seriously undermine the correct

functioning of the electoral system.

The validity of this common-sense intuition crucially depends on the origin of invalid

ballots and the relationship between the fraction of invalid ballots and electoral competi-

tion. In this paper, we study how the closeness of electoral race relates to the fraction of

invalid ballots under the traditional paper-ballot hand-counted voting technology. Using

a large dataset from the Italian parliamentary elections in 1994-2001, we find a strong

robust negative correlation between the margin of victory of the leading candidate over

the nearest rival and the fraction of invalid ballots.

We then investigate the possible theoretical explanations for this relationship and ar-

gue, on the basis of econometric evidence, that this relationship is unlikely to be driven

by voter mistakes, protest, or electoral fraud. The explanation that garners most support

is that election officers and party representatives rationally allocate more effort in detect-

ing invalid ballots when the stakes are highest, i.e. when the electoral race is closer. In

other words, the relationship that we document corresponds to higher rates of detection

of invalid ballots in closer elections.

To the best of our knowledge, this is the first paper that documents and analyzes the

2

relation between electoral competition and invalid ballots. Numerous papers in economics

and political science (e.g. Ansolabehere and Stewart III, 2005, Shue and Luttmer, 2009,

Dee, 2007, Card and Moretti, 2007, Fujiwara, 2011) have studied the electoral outcomes,

including the number of invalid or residual votes, under different voting technologies.1

However, what matters for electoral outcomes is not so much the average level of ballots

counted as invalid under different technologies, but whether the number of (truly) invalid

ballots increases or decreases when the electoral race is closer. Having a substantial

fraction of invalid ballots or misvotes in a landslide election clearly matters less (as noted

by Dee (2007) and Shue and Luttmer (2009) for the California recall election in 2003)

than a much smaller fraction of invalid ballots in a close election (as, for instance, in the

case of misvotes in Palm Beach County, Florida, during the 2000 Presidential election).

This issue is exactly the focus of our paper.

Another related strand of literature studies vote buying and ballot rigging (see the

collection of papers in Schaffer 2007 and Lehoucq 2003 for a good survey). In a fasci-

nating study of Chilean elections before 1965, Baland and Robinson (2008) find that the

introduction of the secret ballot in 1958 has effectively destroyed the “market” for votes

that existed between landed aristocracy and agricultural workers, thus sharply decreasing

the votes for the right-wing parties. Lehoucq and Molina (2002) study the accusation of

ballot-rigging filed in Costa Rica, and find that such accusations where substantially more

numerous in close-race districts. This finding does not, however, imply that fraud is more

frequent in close-race districts: it might as well be that, holding the number of rigged bal-

lots constant, there are higher incentives for parties to file an accusation of ballot-rigging

in close-race districts. Thus, understanding whether the correlation between the fraction

of invalid ballots and the closeness of electoral race is driven by fraud is a crucial question.

The additional contribution of this paper lies in providing an answer to this question.

1 Invalid Ballots: What Are They?

In any election based on a paper ballot system, all ballots cast by voters belong to one

of the three categories: valid, blank (the voter did not express any preference), or invalid

(election officer considers that the voter did not express her preference correctly). Under

1See Stewart III (2011) for an excellent survey.

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the traditional hand-counted paper ballot system, after the vote count is completed, the

election administration reports the number of ballots belonging to each category. A

ballot can be considered invalid for different reasons: for instance, the voter over-votes

(i.e. casts more than one preference when only one preference is allowed) or takes an

action that undermines the secrecy of the vote (e.g. she signs the ballot). The duty

of an election officer is to invalidate any ballot on which the voter does not uniquely

identify her preference. These rules apply to most, if not all, democratic elections using

the paper-ballot system. The stated objective of this procedure is to avoid antidemocratic

and illegal voting behavior.

The Institute for Democracy and Electoral Assistance, which maintains a database

on parliamentary and presidential elections across most countries in the world, reports

that the fraction of invalid votes for about 100 countries over the last 10 years. The

average fraction of invalid ballots is around 3 percent. However, looking across countries

(see Figure 1), one sees a large variation in this measure. In all the developed countries

the fraction of invalid ballots is a single-digit number, typically below 5 percent. The

number is much higher for the developing countries, with double-digit numbers in several

developing countries, in particular in Latin America and Western Africa.

Political scientists have tried to correlate the variation in the fraction of invalid ballots

to some principal characteristics of the political system. Power and Garand (2007) ana-

lyze, using an aggregate-level panel-data analysis from 80 legislative elections held in 18

Latin American democracies between 1980 and 2000, the influence of three sets of factors

on the number of invalid ballots: socio-demographic (literacy, education, wealth), institu-

tional (electoral system and ballot structure), and political (alienation and protest). They

find some support for all the three sets of factors: socioeconomic factors (urbanization

and income inequality) correlate with the number of invalid votes, institutional factors

(compulsory voting, electoral disproportionality, and the combination of high district

magnitude with personalized voting) increase the number of blank and spoiled ballots,

whereas political factors such as political violence and the level and direction of demo-

cratic change also correlate with the fraction of invalid votes. Uggla (2008) also conducts

an aggregate study by looking at over 200 elections in Western Europe, Australia, New

Zealand, and the Americas in the 1980-2000 period. He finds support for the hypothe-

sis that the variation in the fraction of invalid ballots reflect the voters’ reaction to the

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perceived absence of political choice.

The key problem with these aggregate studies is that one cannot rule out the influence

of third unobserved factors (e.g. political culture) that influences simultaneously the

number of invalid ballots and the institutional factors. We are able to overcome this

problem by using highly disaggregated data from a setting with homogeneous formal

political institutions, but with sufficiently large variation (both across time and space) in

political behavior.2

2 Context and Data

2.1 Organization of Italian Parliamentary Elections

In this section, we describe the political and institutional context from which our data

comes. We analyze electoral data from the three Italian parliamentary elections (1994,

1996, and 2001), during which three-quarters of the Chamber of Deputies (the lower

chamber) was elected through the first-past-the-post majoritarian system, in 475 uni-

nominal electoral districts (explained in detail below). We restrict our dataset to this

period because these elections exhibit a natural measure of the closeness of the electoral

competition: the margin of victory between the first and the second candidate.

Our dataset has several advantages over similar data from other settings. First, our

data is highly disaggregated: the unit of observation is a municipality (for the electoral

districts that contain more than one municipality) or an electoral district (for large mu-

nicipalities that contain more than one district); this substantially increases the power of

statistical analysis. Second, it counts separately blank ballots and invalid ballots. This is

important because under the traditional paper-ballot voting, a blank ballot clearly indi-

cates intentional abstention by the voter, whereas in settings that use other technologies

(such as, for instance, in most elections in the U.S.), it is difficult to separate clearly the

voter intention from the malfunctioning of the voting technology, in case of an empty bal-

lot (see Ansolabehere and Stewart III, 2005). In such settings, the election data usually

lumps together blank and invalid ballots into the category of “residual votes.” Third, in

Italian elections, invalid ballots represent a relatively small but non-negligible fraction of

2Two other studies (McAllister and Makkai, 1993, Power and Roberts, 1995) study within-countryvariation in invalid ballots (in Australia and Brazil, respectively). They do not attempt to test alternativehypotheses for the relationship between electoral competition and invalid ballots.

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total votes. However, the quality of democratic institutions and voter literacy are high,

and therefore it is unlikely that the overwhelming majority of invalid ballots are driven

by protest or voter mistake (as, for instance, in most Latin American countries). Finally,

while the electoral system is uniform throughout the country, there is rich geographic

variation in the measures of electoral behavior and outcomes, both across large (regions

and provinces) and small (municipalities and within-city electoral districts) administrative

units.

For three legislatures, the ones that started in 1994, 1996, and 2001, Italian citizens

elected their representatives using a two-tier system (75 percent of representatives via the

majoritarian system and the remaining 25 percent via the proportional system). Before

1994 and after 2001 the entire Italian electoral system was proportional.

On election day, each voter received two ballots: one to cast a vote for a candidate in

her single-member district, and another to cast a vote for a party list in her larger pro-

portional district. Figure 2 shows a typical ballot, for the majoritarian and proportional-

representation systems in Italy. In the districts with the majoritarian system, the voter

has to put a cross on the name of the candidate of her preference, whereas in the districts

under the PR system, she has to put a cross on the party/coalition symbol.

475 out of the 630 House members were elected in single-member majoritarian-election

districts, while the rest was elected from closed party lists in 26 multiple-member districts

(with 2 to 12 seats per district).3 We focus on these 475 majoritarian-election single-

member districts.

The polling stations during the elections operated in the following way. Parliamentary

elections in Italy take place on a Sunday between 8 AM and 10 PM, and on the following

Monday between 7 AM and 3 PM. As soon as the elections end (i.e. on Monday afternoon),

election officers start counting the ballots. The counts typically last uninterrupted until

late Monday night or, sometimes, up to Tuesday morning.

Each polling station has 3 types of election officers: the president of the polling station

a secretary and three canvassers.4 Party list representatives, at most two for each list,

3For the Senate elections, instead, voters received only one ballot to cast their vote for a candidatein a single-member district, and the non-elected candidates with the highest numbers of votes in the232 majoritarian districts were later assigned to the remaining 83 seats according to the proportional-representation rule.

4Our description is based on Article 34 of the Electoral Law (“Testo unico delle leggi per l’elezionedella Camera dei deputati”), approved by the Decree of the President of the Republic on 30 March 1957

6

can also assist the vote count. At least three election officers, including the president

or the vice-president (chosen by the president among the canvassers), have to be present

through the entire count. The president of the polling station decides (after consulting the

canvassers) on the outcome of any disputes related to the vote count, including those about

the validity of any given ballot. She then registers her provisional decision (the Parliament

has the last word about official protests). The secretary keeps the official record about

all the activities during the count. At the end of the counting all members of the polling

stations sign the record. Both the election officers and party list representatives can

contest ballots, i.e. question the decision about the validity of any given vote.

When working at the polling stations, each election officer receives a monetary com-

pensation which corresponds, approximately, to 100 euros. In addition, both election

officers and party representatives are compensated by their employers with (at most) 3

days of paid leave.

Each ballot is scrutinized by all the canvassers, the president, and - if present - by party

representatives. The number of valid votes for each candidate are marked (typically on

the board) and regularly updated as the count proceeds. This implies that people present

at the count can observe the evolution of the number of votes for each candidate, and

have a perception of the margin (at their polling station) between the leading candidate

and the nearest rival.

Given that voters are instructed to put just one sign (“x”) on the ballot (no other

mark is allowed), detection of any visible irregularity on the ballot (e.g. more than one

preference expressed, a signature, an additional mark made by mistake) implies that the

president declares the ballot as invalid. However, given the large number of ballots that

have to be scrutinized and the fact that often the count continues late into the Monday

night, there is no guarantee that each ballot containing an irregularity (e.g. a minor

additional sign) gets detected.

According to the Electoral Law the president is a public official and has the authority

to arrest those who disturb the voting process, including the party representatives and

the other canvassers. The president, the secretary and the canvassers are all obliged to

denounce any criminal act related to the voting and the vote counting. If the president

is involved in such acts, the secretary and the canvassers are supposed to contact the

(No. 361).

7

judicial authorities. Public officials who deliberately alter the ballots or the final counting

risk between 2 and 8 years of jail.

2.2 Data

We extracted information on three majoritarian parliamentary elections from the Histor-

ical Electoral Atlas of Italy (Corbetta and Piretti, 2008). An observation in our dataset

represents the smallest level of aggregation of polling stations available, that is the small-

est unit between a municipality and a district (hereafter, we refer to this as ‘the electoral

unit’). Larger cities have several districts: for instance, the municipality of Rome has

24 and the municipality of Milan has 11. In most cases, several municipalities (there are

more than 8,000 of them in Italy) belong to the same district.

Each polling station is responsible for 500 to 1,200 eligible voters, though there can be

exceptions to this rule for isolated territories that are hard to reach. While in general we

do not know whether an electoral unit corresponds to a polling stations, electoral units

with an electorate that is smaller than 1,200 (there are 32 percent of such units) are, due

to the previous rule, likely to be single polling stations. In order to avoid any selection

based on the size of the electorate we are going to use all the electoral units and later

check whether the results are robust to the use of electoral units that are likely to be

single polling stations.

Table 1 presents the summary statistics for the key variables used in our empirical

analysis. Overall, our dataset contains 8,224 electoral units for the three election years,

which gives a (slightly unbalanced) panel of 23,126 observations. Our main variable of

interest, i.e. ballots reported as invalid, represent a non-negligible fraction of votes. On

average, in a typical district or municipality, 3.9 percent of all the ballots is reported as

invalid. We also see that there is substantial variation in this measure: the standard

deviation is 2.2 percent. A slightly higher fraction of ballots (4.6 percent) is cast blanc.

Turnout rate is relatively high (which is a traditional characteristic of Italian elections): in

a typical district, 82 percent of all eligible voters participate. The average leading margin

is substantial, at the electoral unit level (i.e. the difference in share of votes between

the candidate with the highest number of votes and the nearest rival) is 18.4 percent;

however, the variation is large (the standard deviation is 14.8 percentage points). The

electoral unit with the smallest leading margin in our dataset exhibits a vote difference

8

of zero percent, whereas in the one with the largest margin, the first candidate leads by

96.1 percent.

The main two party coalitions (center-left and center-right) lead the electoral compe-

tition in most electoral units (in a typical unit, they obtain 36.2 and 38 percent of votes,

respectively). We observe a strong party incumbency effect: in 94.4 per cent of cases, the

candidate from the incumbent coalition is the one with the highest number of votes. The

incumbent politician effect is, however, much smaller: in 46.5 percent of cases, the voting

ballot contains the name of the incumbent politician, and in slightly more than half of

these cases (or in 26.4 percent of the total), the incumbent politician leads. The number

of candidates also varies across districts. On average, a voter is confronted to a ballot

with 4.14 candidates.

Figure 3 indicate that the fraction of invalid ballots varies substantially across different

regions. Southern regions exhibit the highest levels of invalid ballots, followed by the

North-West. The Northern and Central regions exhibit the lowest levels of invalid ballots.

While North-South divide is large, there is also substantial region-level variation within

the North and the South of Italy.

3 Invalid Ballots and Electoral Competition

Figure 4 presents graphically the relationship between the leading margin (the difference

in share of votes between the candidate with the highest number of votes and the nearest

rival) and the fraction of ballots reported as invalid (out of the total number of ballots).

Each dot represents the fraction of invalid ballots for a given percentile of the margin of

victory. For the levels of leading margin that are close to zero, invalid ballots represent

almost 4.5 percent of all votes, whereas to the largest percentiles of the leading margin

correspond the lowest fractions of invalid ballots (around 2.5 percent). Overall, there is

a clear negative correlation between the two variables: the larger is the leading margin,

the smaller is the fraction of invalid ballots. This is also confirmed in column 1 of Table

2: the regression coefficient on the leading margin is negative and highly statistically

significant.5 The effect is quantitatively important: one standard deviation increase in

the leading margin (14.8 percentage points) corresponds to a reduction in the fraction of

5This result is robust to using the logarithms of the variables instead of their levels on one or bothsides of the regression equation.

9

invalid ballots of about one-sixth of a standard deviation (0.35 percent of total votes).

Restricting the analysis to the 2,704 electoral units with less than 1,200 eligible voters

leads to very similar results (see Table 3).

4 Competing Explanations

What are the possible explanations for the empirical relationship that we have established

above?

The prime suspect is the behavior of voters. Consider a simple cost-benefit calculation

of an individual voter. Suppose that filling out the ballot requires concentration, and filling

it out correctly implies some attention cost. Moreover, suppose that the probability

of making a mistake (and, therefore, submitting an invalid ballot) decreases with the

attention allocated by the voter. On the benefit side, if the voter prefers one candidate

over the other, she might perceive a benefit from feeling that her vote helped to increase

the chances of victory of her preferred candidate. This might be justified by either the

fact that a voter considers her probability of being pivotal (see Ch. 14 in Mueller 2003),

or - more realistically - by the fact that the voter might feel the moral duty to “do her

part” in helping her preferred party to win (as in the models by Feddersen and Sandroni

2006a,b).

The higher is the expected margin of victory of one of the candidates in the district,

the lower is the voter’s expected benefit of casting a valid vote. Given that the margin of

victory does not affect the cost side, the higher is the margin, the lower is the attention

that the voter devotes to casting a valid vote, and thus the higher is the probability of

submitting an invalid ballot.

Under this simple opportunity-cost theory of voter behavior, we would obtain a pre-

diction that a higher margin of victory should be positively correlated with the fraction

of invalid ballots. However, as we have seen above, the relationship is negative. Thus,

this correlation cannot be explained by voters’ attention.

Another explanation is based on voter protest. Voters might have feelings about the

choice that they are facing, and may act in the voting booth in reaction to these feelings.

For instance, Brighenti (2003) analyzes a selection of invalid ballots in a regional election

in Italy, and finds that a part of the invalid ballots report emotionally-charged (typically,

10

negative) messages written by voters on their ballots. These are examples of voluntary

invalidation.

If the expected margin of victory is sufficiently large, some of the voters that support

the losing candidate might feel that, de facto, their electoral choice is constrained. If this

triggers negative emotions in them, some of the voters might voluntarily invalidate their

ballots. A related possibility is that of expressive voting (Brennan and Lomasky, 1993,

Schuessler, 2000). If voters want to express their general discontent about the political

system, they might want to cast an invalid ballot as a protest. At the same time, each

voter might have a political preference for some party. The closer is the electoral race,

the higher is the opportunity cost of invalidating the ballot to express one’s discontent.

Under this theory as well, we should observe a positive correlation between the margin of

victory and the fraction of invalid ballots (which goes against what we find in the data).

We can further refine our analysis, if we consider that ballot invalidation is not the

only way of expressing one’s protest. Some of the voters might express their feelings by

leaving their ballots blank. Then, the fraction of invalid ballots and that of blank ballots

should be correlated. Based on this intuition, we can use the fraction of blank ballots as

a regressor, so as to capture, at least in part, the voters’ protest.

Our empirical results show that this explanation based on voter protest does not fit

the data. First, in columns 1 and 2 of Table 2, the coefficient on the leading margin is

negative (which is the opposite to the prediction of this theory). Second, while blank

ballots correlate positively with the fraction of invalid ballots, even when we include the

blank ballots and the number of candidates in the regression, the negative coefficient on

the leading margin remains highly statistically significant.

In column 3, we verify how robust our main finding is to the inclusion of a series of

local (province-level) characteristics that can affect the benefits and costs for voters of

casting valid ballots: the level of education (measured by the fraction of the population

with university and high-school degrees), social capital (measured by the average turnout

at national referenda), income (measured by labor activity and unemployment rates, and

GDP per capita), crime (the extent of mafia-related crimes), and urbanization. While

some of these variables capture a part of the variation in invalid ballots, the coefficient

on the leading margin remains highly significant. In column 4, we perform an even

more stringent test, by adding year and electoral unit fixed effects. This means that the

11

remaining variation in invalid ballots is within the same electoral unit (the smallest unit

between the municipality and the district) over time. The coefficient on the leading margin

remain basically unchanged (both in terms of size and significance). In other words, if the

leading margin increases from one election to the other within the same electoral unit,

the fraction of invalid ballots reported at this unit decreases.

Logically, if the explanation for the negative correlation that we observe cannot come

from voters’ behavior, it should come from the behavior of those who count the votes,

i.e. election officers. Let’s suppose that election officers act rationally. Given that they

are called to act as public officials to ensure that all the ballots cast are counted correctly

(which, in particular, includes detecting ballots that are cast incorrectly), we can model

the problem of the officer as follows.6

Suppose that each officer considers all the ballots that have to be counted, one by

one. Each ballot that he scrutinizes can be either valid or invalid. The objective of the

election officer is to minimize the likelihood that the victory is incorrectly adjudicated to

the candidate that, in reality, has fewer valid ballots in her favor. However, the officers

might make mistakes. There are two types of error that the officer might commit. Type

I error consists in invalidating a truly valid ballot. Type II error consists in counting

as valid a ballot which is in reality invalid. Given that the type I error is very unlikely

to happen (it is impossible to see a non-existent irregularity in a ballot which has been

correctly filled out by the voter), we can assume such errors away. Instead, the type II

error - missing an existing irregularity - is much more important. Moreover, the likelihood

of this error is affected by the effort that the officer exerts. These type-II errors might

jeopardize the true outcome of the elections if they are sufficiently numerous as compared

to the difference in the number of valid votes between the two candidates.7

In other words, the officer exerts the effort of attention to minimize the number of

type-II errors. However, the effort is costly, and the higher is the number of ballots

to scrutinize, the higher is the marginal cost of effort. On the other hand, the risk of

jeopardizing the election outcome depends on the expected margin of victory: the higher

6In the Appendix, we present a simple formal model of an election officer’s behavior, along the linesdiscussed here.

7This implicitly assumes that the election officer acts taking into account the worst-case scenario: that,if let pass, all the invalid ballots are counted as votes for the same candidate. While this assumption isunrealistic in its pure form, our reasoning remains valid as far as the election officer considers as possiblea scenario sufficiently close to the worst case.

12

is this margin, the less it is likely that a given number of type-II errors influence the

election outcome.

The rational officer chooses the level of effort that equates the marginal cost of effort to

its marginal benefit. If the expected margin of victory increases, the benefit of effort falls,

and thus the officer puts lower effort. This, in turn, implies a lower number of truly invalid

ballots that are counted as invalid. Thus, this theory can explain the negative correlation

between the margin of victory and the fraction of invalid ballots: election officers rationally

allocate effort, depending on the (expected) closeness of elections, which implies higher

rates of detection of invalid ballots in relatively closer races.

Let’s now consider the effect of a variation in turnout. Given that the number of

election officers is fixed (i.e. it is not adjusted on the basis of turnout), a higher number

of voters showing up at the polls implies a higher number of ballots that each officer

has to scrutinize. This means (under the standard convexity assumption on the cost

function) that the incremental cost of effort increases. The officer then finds it optimal

to reduce the effort that she puts in scrutinizing the ballots, which, in turn, leads to a

lower fraction of invalid ballots. Moreover, this effort-reducing effect is stronger when

the electoral competition is weaker. Thus, we should observe that the fraction of invalid

ballots is negatively correlated with higher voter turnout, and that the negative correlation

between invalid ballots and margin of victory is stronger for higher-turnout electoral units.

Table 4 reports the estimates with this interaction term included in the regression.

Consistent with the above hypotheses, we indeed find that the coefficients on turnout and

the interaction between turnout and leading margin are negative and highly statistically

significant. Both coefficients remain significant when we add year fixed effects (column

2). Notably, the coefficient on the interaction term remains significant (and even increases

in absolute value) in the most stringent specification (column 3), i.e. when we add both

the year fixed effects and the electoral unit fixed effects (the coefficient on turnout loses

significance, probably because the within-unit variation in turnout is fairly small).

The explanations above disregard the role of political parties. However, as we discussed

in the previous section, party representatives can attend the vote count, and it is highly

plausible that parties act strategically in this respect and try to actively use their resources

to influence the intensity of vote counting, depending on the incentives. In particular,

if the total number of representatives that each party can allocate to any given election

13

is limited (parties either have to pay the representatives to do this job, or to mobilize

volunteers), parties are likely to allocate their representatives in units that give them the

highest expected return.

The institutional organization of the electoral system allows us to obtain a set of

additional predictions. For candidates, what matters is not winning the race at each

municipality, but to obtain the highest number of votes at the district level. However, the

closeness of electoral race at the district level does not necessarily coincide with that in

each electoral unit within that district. Election officers do not have access to information

about the evolution of the vote count in other units (and thus at the district level), they

have to use the vote numbers in their own units as the best predictors of what happens at

the district level. Parties, however, have a clear informational advantage in this respect.

Clearly, allocating representatives (even in locally competitive races) in districts that

are won or lost almost for sure (i.e. those with wide expected margins of victory at

the district level) makes little strategic sense. Thus, parties allocate disproportionately

more representatives - in both locally competitive and non-competitive units - in districts

where the (district-level) competition is more tight, and where even a few votes counted

mistakenly might imply winning or losing the parliamentary seat. Then, in a two-party

elections, if both parties act similarly, we should expect that ballots are scrutinized much

more closely in the districts with lower victory margins. This would imply a higher

fraction of ballots invalidated in such districts, and this, independently of the closeness

of the electoral race at the unit level.

We start exploring the role of parties in Table 5, by comparing the regression coef-

ficients for specifications with and without the dummies for the identity of the leading

coalition (center-right and center-left). Column 1 is the same specification as the one

reported in column 4 of Table 2. In column 2 we add the dummies for the identity of

the leading coalition. We see that the coefficient on the leading margin does not change;

however, when the leading coalition is the center-right one, the fraction of invalid ballots

is significantly smaller. This could be because center-right coalition has more resources to

devote to observing the vote counts (note that the specification includes the electoral unit

fixed effects; therefore, the remaining variation is within units, so this right-wing effect

cannot be driven by fixed characteristic of voters at the unit level).

Column 3 includes the measure of electoral competition at both the local and district

14

level. We see that the increase in either leading margin significantly reduces the fraction

of invalid ballots. In column 4 we also add the interaction term between the two margins.

The coefficient on the interaction term is negative and highly statistically significant.

What does this mean? Figure 5 resumes this finding in the graphical form. Defining

a race to be competitive at the district level when the margin of victory is below the

overall median margin of victory across all districts and elections, the slope of the rela-

tionship between the fraction of invalid ballots and the (unit-level) leading margin is very

different in competitive and non-competitive parliamentary districts. In particular, in

non-competitive districts, larger leading margin at the electoral unit level implies smaller

fraction of the invalid ballots. This is consistent with the explanation of the rational allo-

cation of detection effort by election officers, who do not observe what happens in other

units and thus consider their own units as representative of the district-level race. Con-

trarily, in competitive districts, larger leading margins at the electoral unit level do not

lead to the reduction of invalid ballots. This is likely to be because of the attention that

party representatives devote to all (or most) electoral units in such districts, regardless of

the intensity of competition locally. Party representatives thus keep putting pressure on

election officers so that these latter detect all the invalid ballots possible, even in units

with large local margins, given that the race is very close at the district level.

In the above discussion, we have implicitly assumed that election officers are motivated

by duty. A plausible alternative is that they have preferences over candidates or parties,

and - given the difficulty to monitor their behavior during the count - try to help their

preferred candidates or parties to win by invalidating some of the valid ballots that are in

favor of their less-preferred candidates. Researchers in political science have been aware of

this possibility for a long time. For example, in his analysis of voting in the U.S. elections,

Harris (1934) writes:

“The use of paper ballots undoubtedly is conducive to voting frauds. The

paper ballots must be counted by hand, frequently requiring several hours or

longer, under conditions late at night which are likely to facilitate frauds. The

election officers are quite exhausted after the long day at the polls, and are

not fit to carry on the count for hours afterwards. The watchers are likely

to leave if the count lasts for hours, and various short cuts may be used. In

15

the confusion, poor light, mingling of ballots, etc., it is easy for ballots to be

altered or substituted, and for the count to be falsified. If the ballot is short

and the count can be completed within a very few hours, these dangers are

not present” (Harris, 1934, pg.380)

Given that electoral fraud is an illegal activity, it implies the risk of getting punished

if the illegal action of the election officer is discovered. Unless the three canvassers, the

secretary, the president, as well as the party representatives that are present in the polling

station agree to forge the elections, the decision problem of a law-breaking officer can be

described as follows. Each incremental valid ballot that the officer invalidates increases

the risk of getting caught. Moreover, it is plausible to assume that this risk increases

more than proportionally with each additional ballot. If the officer invalidates just a few

valid ballots, the likelihood that the authorities discover this misbehavior are very low.

However, if she invalidates a few more ballots, this likelihoods starts to increase relatively

quickly, as - for instance - the discrepancy of the election outcomes with exit polls starts

to increase.

On the benefit side, the biased officer wanting to increase the likelihood that her pre-

ferred party wins the election understands that this likelihood is large when the expected

margin of victory of one candidate over the other is slim. Contrarily, when the expected

margin of victory is wide (either in favor of her preferred candidate or against), additional

invalidated ballots do not contribute to increasing this likelihood. Given that the risk of

getting caught for invalidation does not depend on the expected margin of victory, wider

expected margin of victory implies lower number of invalidations by the biased officer.

This explanation predicts that higher margin of victory should be negatively correlated

with the fraction of invalid ballots, just like the explanation based on duty-driven election

officers that we have described above.

How can one discern empirically between these two alternative explanations? Suppose

that the electoral fraud is an important driver of the variation in invalid ballots. Under an

auxiliary assumption that the extent of electoral fraud is correlated with other measures

of crime, we then should normally observe a stronger effect of electoral competition on

invalid ballots in areas with higher rates of crime. We report in Table 6 the results of the

estimations in which we add as regressors different measures of crime (at province level),

16

as well as the interaction terms between crime rates and margin of victory. If the electoral

fraud mechanism is empirically important, we should find a significant negative coefficient

on the interaction term. In neither of the three specifications (in which crime is measured

with the rate of extortions, mafia-related crimes, and total crimes) the coefficient on the

interaction term is statistically different from zero. We can see this clearly also on Figure

6, in which we plot the relationship between electoral competition and invalid ballots in

high-crime and low-crime areas. Independently of how we measure the crime rates, the

slopes of the relationship between electoral competition and invalid ballots in two areas

are very similar. This implies that electoral fraud cannot be the leading explanation for

the empirical relationship that we have established.

5 Conclusion

Invalid ballots have been considered a problem for democratic elections, as they might

jeopardize the electoral outcome when the electoral race is close. This paper challenges

this view. Using a detailed micro-level dataset from the Italian parliamentary elections

in 1994-2001 (which use the traditional paper-ballot hand-counted voting technology),

we find a strong robust negative correlation between the margin of victory of the leading

candidate over the nearest rival and the fraction of invalid ballots. We then show that this

relationship is unlikely to be driven by voter mistakes, protest, or electoral fraud. The

explanation that garners most support is that election officers and party representatives

rationally allocate more effort in detecting invalid ballots when the stakes are higher, i.e.

when the electoral race is closer. In other words, under hand-counted voting technology,

in closer elections there are higher rates of detection of invalid ballots.

Our findings imply that the traditional paper-based hand-counted ballot system seems

to has a correction mechanism that adjusts the likelihood that the victor is announced cor-

rectly to the closeness of electoral race. This mechanism functions thanks to the increased

attention that the election officers and parties allocate to making sure that invalid ballots

are not counted as valid ones when the electoral race becomes closer. Clearly, in machine-

counted voting systems such correction is absent (unless vote re-counting by hand is added

to the machine count in districts with particularly close elections). Thus, while it is true

that hand-counting technology is more expensive than the alternatives in settings where

17

there are relatively frequent elections at many levels, such as the US (Stewart III, 2011),

this higher cost should be evaluated against the benefit of this correction mechanism that

we have established in this paper.

Natural next steps are to investigate whether similar behavior is present in other

settings where ballots are counted by hand, as well as quantifying the benefit of the

correction mechanism as compared to other voting technologies. This would then allow

to design a fully fledged welfare evaluation of the recent voting-technology reforms.

18

6 Appendix

In this Appendix, we construct a simple formal model of the behavior of an civic-duty

motivated election officer.

The officer’s objective function is to maximize her utility, which consists of two terms.

The first term captures the fact that she wants to reduce the risk of jeopardizing the

true outcome of the elections. The probability of this event depends negatively on the

effort exerted by the officer when scrutinizing the ballots. The second term represents the

standard convex cost of effort.

Let’s denote with n the number of true invalid ballots. Faced with a ballot (valid or

invalid), the officer might commit one of the two type of errors. Type I error consists in

invalidating a valid ballot. Type II error consists in counting as valid a ballot which is

truly invalid. Given that the type I error is very unlikely to happen (one can hardly spot

an inexistent irregularity in a ballot correctly filled by the voter), we will assume these

errors away. Instead, the type II error, i.e. missing an existing irregularity, is much more

important and the probability of this error is affected by the effort that the officer exerts.

Let’s denote this probability with p.

These type-II errors might jeopardize the true outcome of the elections if they are

sufficiently numerous as compared to the difference in the number of valid votes between

the two candidates with the highest number of votes. Let’s denote with d and de the

true and the expected difference in the number of valid votes between the two candidates,

respectively. Let’s assume, moreover, that

d = deε, (1)

where ε is the noise which is a random variable drawn from a uniform distribution:

ε ∼ U

[

1− 1

2φ, 1 +

1

2φ

]

. (2)

Then, the problem of the officer can thus be written as:

maxx

U = −Pr [np(x) > d]− c(x, α), (3)

where α is the parameter that captures the election-specific objective difficulty of scrutiniz-

ing the ballots (for instance, it is higher in a district with a larger number of candidates).

19

Using (1) and (2) in (3), and dropping the constant terms, the problem becomes

maxx

− φ

denp(x)− c(x, α). (4)

The first-order condition of this problem is

− φ

denp′ (x) = cx(x, α). (5)

The left-hand side is the marginal benefit of effort, measured in terms of reduced risk

of jeopardizing the true election outcome. Higher effort reduces the probability of error by(

− dp

dx

)

, for each invalid ballot. Given that there are n truly invalid ballots, this translates

into n(

− dp

dx

)

less miscounted ballots. The lower is the expected vote difference between

the two candidates with the highest number of votes (lower de) and the higher is the

precision of the estimate of the vote difference (higher φ), the higher is the effect of this

reduction in miscounted ballots on the risk of jeopardizing the true election outcome. The

right-hand side simply represents the increasing marginal cost of effort.

From (5), we easily get the comparative statics on the optimal effort of the officer:

x∗ = x(+

φ,−

de,+n,

−

α). (6)

Higher number of truly invalid ballots and a higher precision of the estimate of the vote

difference increase the effort of the officer. Higher expected vote difference and the steeper

increase in the cost of effort reduce the effort of the officer.

To get a closed-form solution that is needed for x∗ to have a tractable empirical spec-

ification, we assume that p (x) has the shape of the exponential cumulative distribution

1 − eλx, with λ > 0, and that the cost function has the shape of an exponential func-

tion c(x, α) = eαx − 1, with α > 0. Without loss of generality, we assume that α > λ.

These functions fit our purpose particularly well, given that they capture the decreasing

returns to effort for the probability of committing the type-II errors and the more than

proportional cost of effort. With these functional forms the first-order condition becomes:

φ

denλeλx = αeαx,

and, solving for x∗, we obtain

x∗ =1

α− λlog

(

φnλ

deα

)

.

20

Empirically, we can not observe the officer’s effort directly, but only the number of

ballots reported as invalid. In terms of our model, denoting this number as nv, we get

nv = n [1− p(x∗)] = nv(+

φ,−

de,+n,

−

x), (7)

which, taking logs, becomes

lognv = log n+ λx∗ = log n+λ

α− λlog

(

φnλ

deα

)

(8)

= a + b1 log de + b2 log n+ e, (9)

where a = − λ

α−λlogα, b1 = − λ

α−λ, and b2 = α

α−λ, and e is an unobserved component

equal to λ

α−λlog φ.

Three points are worth noting. First, a higher vote difference (between the two candi-

dates with the highest number of votes) negatively correlates with the number of reported

invalid ballots, i.e. b1 = − λα−λ

< 0. Second, a higher number of invalid votes positively

correlates with the true number of reported invalid ballots, i.e. b2 = αα−λ

> 0. Finally,

for higher values of α (i.e. when the cost function is steeper) the number of invalid votes

decreases.

21

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24

(7.3,22.85](5.13333,7.3](3.74333,5.13333](2.956,3.74333](2.2,2.956](1.55,2.2](1.20833,1.55](.8,1.20833][0,.8]No data

Figure 1: Invalid ballots (as a fraction of total ballots) in the parliamentary electionsaround the world

Source: Institute for Democracy and Electoral Assistance (www.idea.int)

25

http://www.idea.int/

Figure 2: A typical ballot in Italian parliamentary elections

26

[2.42,2.86](2.86,3.17](3.17,3.57](3.57,3.84](3.84,3.99](3.99,4.66](4.66,4.74](4.74,5.49](5.49,7.53]

Figure 3: Invalid ballots (as a fraction of total ballots) in Italian parliamentary elections,1994-2001 (majoritarian districts)

Notes: Author’s calculation based on Italian national elections data (Corbetta and Piretti, 2008).

27

.025

.03

.035

.04

.045

Fra

ctio

n of

inva

lid b

allo

ts

0 .2 .4 .6Leading margin of the 1st candidate over the 2nd

Invalid ballots, margin between 1st and 2nd candidate

Figure 4: Fraction of invalid ballots by percentile of leading margin


28

.02

.03

.04

.05

.06


Non−competitive district Competitive districtlinear fit linear fit

Invalid ballots, margin between 1st and 2nd candidate

Figure 5: Fraction of invalid ballots by percentile of leading margin and district-levelcompetition


.02

.03

.04

.05


Above median Below medianlinear fit linear fit

Invalid ballots and leading margin (Crime : mafia)

.02

.03

.04

.05



Invalid ballots and leading margin (Crime : extorsions)

.02

.03

.04

.05



Invalid ballots and leading margin (Crime : total)

Figure 6: Fraction of invalid ballots by percentile of leading margin, in high-crime versuslow-crime provinces


29

Table 1: Summary statistics

Variable Mean Std. Dev. Min. Max. N

Invalid ballots 0.039 0.022 0 0.573 23109Blank ballots 0.046 0.022 0 0.245 23109Turnout 0.820 0.108 0.049 1 23109Leading margin (municipality/district) 0.184 0.148 0 0.961 23109Leading margin (district) 0.139 0.124 0 0.756 23109Right coalition leads 0.38 0.485 0 1 23109Left coalition leads 0.362 0.481 0 1 23109Incumbent party leads 0.944 0.23 0 1 15020Incumbent leads 0.264 0.441 0 1 15020Number of candidates 4.136 1.005 2 9 23109

30

Table 2: Basic regression results

(1) (2) (3) (4)Fraction of invalid ballots

Leading margin at electoral unit level -0.024*** -0.018*** -0.013*** -0.014***(0.002) (0.002) (0.002) (0.002)

Turnout -0.047*** -0.007 0.016(0.006) (0.008) (0.091)

Blank ballots 0.209*** 0.145*** 0.135***(0.020) (0.019) (0.046)

Number of candidates -0.001 -0.002*** -0.001(0.000) (0.000) (0.001)

Provinces with mafia-related crimes -0.001(0.001)

Fraction of pop. with university degree 0.019(0.182)

Fraction of pop. with high school degree -0.114**(0.054)

Turnout at national referenda -0.000***(0.000)

Labor activity rate -0.054**(0.025)

Unemployment rate 0.064***(0.017)

GDP per capita 0.001(0.002)

Rate of urbanization 0.011**(0.005)

Year FE√

Electoral unit FE√

Observations 23,126 23,126 21,733 23,126R-squared 0.028 0.158 0.269 0.703

NOTE.– Standard errors, clustered at the district level, are reported in parentheses (there are 475majoritarian districts). There are 8,224 electoral-unit fixed effects. *,**, and *** denote statisticalsignificance at 10%, 5%, and 1% level.

31

Table 3: Basic regression results for electoral units with less than 1,200 eligible voters

(1) (2) (3) (4)Fraction of invalid ballots

Leading margin -0.018*** -0.014*** -0.014*** -0.009***(0.003) (0.003) (0.003) (0.003)

Turnout -0.031*** -0.012* -0.040*(0.007) (0.007) (0.021)

Blank ballots 0.165*** 0.143*** 0.133***(0.022) (0.020) (0.027)

Number of candidates -0.001 -0.002*** -0.001(0.001) (0.001) (0.001)

Provinces with at mafia related crimes -0.001(0.002)

Fraction with uiversity degree -0.177(0.264)

Fraction with high school degree -0.046(0.083)

Turnout at referenda -0.000**(0.000)

Activity rate 0.019(0.044)

Unemployment rate 0.044*(0.023)

GDP per capita 0.001(0.005)

Rate of urbanization 0.014**(0.007)

Year FE√



NOTE.– Standard errors, clustered at the district level, are reported in parentheses (there are 475majoritarian districts). There are 2,704 electoral-unit fixed effects. *,**, and *** denote statisticalsignificance at 10%, 5%, and 1% level.

32

Table 4: Regression results with interaction terms

(1) (2) (3)

Fraction of invalid ballots

Leading margin at electoral unit level 0.005 0.012 0.036*(0.020) (0.019) (0.020)

Turnout -0.047*** -0.048*** 0.016(0.006) (0.007) (0.091)

Blank ballots 0.210*** 0.208*** 0.135***(0.020) (0.020) (0.046)

Number of candidates -0.001 0.000 -0.001(0.000) (0.000) (0.001)

Leading margin × Turnout -0.037** -0.038** -0.046**(0.018) (0.018) (0.019)

Leading margin × Number of candidates 0.002 0.001 -0.003*(0.002) (0.002) (0.002)

Year FE√ √


Observations 23,109 23,109 23,109R-squared 0.159 0.169 0.704

NOTE.– Standard errors, clustered at the district level, are reported in parentheses(there are 475 majoritarian districts). *,**, and *** denote statistical significance at10%, 5%, and 1% level.

33

Table 5: Invalid ballots and competition at electoral-unit and district levels

(1) (2) (3) (4)

Fraction of invalid ballots

Leading margin at electoral unit level -0.014*** -0.014*** -0.009*** -0.008***(0.002) (0.002) (0.002) (0.002)

Leading margin at district level -0.010* 0.004(0.006) (0.008)

Interaction between the margins -0.057***(0.016)

Turnout 0.016 0.018 0.019 0.020(0.091) (0.091) (0.091) (0.091)

Blank ballots 0.135*** 0.131*** 0.132*** 0.130***(0.046) (0.047) (0.047) (0.047)

Number of candidates -0.001 -0.001 -0.001 -0.001(0.001) (0.001) (0.001) (0.001)

Right coalition leads -0.005*** -0.005*** -0.004***(0.001) (0.001) (0.001)

Left coalition leads -0.002 -0.002 -0.001(0.001) (0.001) (0.001)

Year FE√ √ √ √

Electoral Unit FE√ √ √ √


NOTE.– Standard errors, clustered at the district level, are reported in parentheses (thereare 475 majoritarian districts). *,**, and *** denote statistical significance at 10%, 5%, and1% level. There are 8,224 electoral-unit fixed effects.

34

Table 6: Invalid ballots, electoral competition, and crime

(1) (2) (3)Fraction invalid ballots

Leading margin at electoral unit level -0.013*** -0.013*** -0.013***(0.002) (0.002) (0.002)

Extorsions (rate X 1,000 inh.) 0.294(1.068)

Mafia related crimes (rate X 1,000 inh.) 0.005**(0.002)

Total crimes (rate X 1,000 inh.) 0.000(0.001)

Interaction between lead. margin and crime -0.108 -0.006 -0.000(0.098) (0.005) (0.000)

Turnout 0.024 0.018 0.024(0.100) (0.091) (0.100)

Blank ballots 0.141*** 0.135*** 0.141***(0.049) (0.047) (0.049)

Number of candidates -0.001 -0.001 -0.001(0.001) (0.001) (0.001)

Year FE√ √ √

Electoral Unit FE√ √ √

Observations 21,716 23,109 21,716R-squared 0.705 0.704 0.705

NOTE.– Standard errors, clustered at the district level, are reported in parentheses (thereare 475 majoritarian districts). *,**, and *** denote statistical significance at 10%, 5%, and1% level. There are 8,224 electoral-unit fixed effects.

35

invalid ballots and electoral competition

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